Research is concentrated in several areas of nonparametric statistics with applications to biomedicine. The study of nonparametric multiple comparisons was continued in FY85. A paper with J. H. Skillings comparing various procedures for determining pairwise differences among treatments has been accepted for publication. The development of distribution-free procedures for data to which weights have been attached is under investigation. The weights arise in biomedical settings through covariates or estimated probabilities or genetic information. The large-sample theory for weighted U-statistics is being developed and, in a particular application, compared with the computer simulated small-sample distribution. The study of proportions is also being continued. A paper on incomplete correlated proportions has recently appeared. Work is continuing on a general theory for modeling the correlation structure of proportions. These developments along with their accompanying specialized computer programs have many applications to biomedical data expressible as proportions.